WARNING! *CONTAINS SPOILERS*
Once you reach the Endgame of Part 4, you'll notice that at the second battle the Black Knight is ready for you, with his own army as well. Ike will go crazy and run to him. Tibarn ((if you brought him with you)) will fly up and want to kill the Black Knight, too. Unfortunately, you'll have to do this with Ike. A wall will come up so that only Ike can fight the Black Knight, and anybody else will be on the other side fighting the Black Knight's army.
Now, I will say straight out, this battle is extremely easy. If you follow my directions correctly, this will probably be the easiest boss in the game, I did it in 3 turns.
For the first turn, DO NOT MOVE IKE! Ike had a terrain advantage right where he is. For me, he would deal 5 damage twice when I move, though when I'm in the same spot I start in, he does 15 damage twice. As long as the Black Knight doesn't use Eclipse, you'll be fine (though if you have Nihil with Ike it won't be a problem.)
In the meantime, with the other army just whack a few heads for experience points.
And there you have it, the easy way to defeat the Black Knight.
Enjoy!